New Here Bare with me

[RockThis52]

I have no idea where to post this so I thought that this would be the most appropriate (hope I'm right)

Alright so my grade 11 teacher is real crap and he can't really teach well. I'm relatively smart in math high 80's and low 90's. But this year he's really bad. We're doing function notation and parent functions, transformations, reflections, stretches compressions and what not.

Here is my real question...

The textbook gives me this question...

The graph of g(x) ?x is reflected across the y-axis, stretched vertically by the factor of 3, and then translated 5 units right and 2 units down. Draw the graph of the new function and write it's equation.

Let's skip the drawing of the graph.

This is what I got... f(x)=3[-(x-5)] -2

According to the textbooks answers the correct answer is...

y=3g[-(x-5)] - 2

I really don't see what I got wrong.

And since my teachers bad, I didn't QUITE get the whole function notation part. That is I don't know how to go from a regular equation to function notation and vice versa.

All I know is that f(x) replaces "y" unless my teachers wrong.

I'm sorry about the total load of questions as I did read the FAQ saying I shouldn't ask a lot but I'm just real stumped. If you don't understand one thing everything else is a mess.

 

[mmm4444bot]

g(x) ?x This looks like a typographical error.

It's supposed to be an equation, yes?

This is what I got... f(x) = 3[-(x-5)] - 2

Is this another typographical error? Where is the name 'g' ?

If you did not intend to write function notation, did you forget to type the radical sign somewhere ?

According to the textbooks answers the correct answer is...

y = 3 g[-(x-5)] - 2

This looks correct.

g[-(x - 5)] is function notation for the horizontal shift and the reflection across the vertical axis.

Subtracting 5 from a function input shifts the graph to the rght 5 units.

Changing the sign of a function input reflects the graph across the vertical axis.

After this, multiplying the output by a factor of 3 stretches vertically, and subtracting 2 shifts the graph vertically down 2 units.

Your textbook should explain and provide examples for all of the different types of function transformations, as well as how they arise. (Or, is your book "bad", too?)

Function notation is a nifty way to express more information than simply writing "y".

Here are some quick comments, off the top of my head.

y = x + 4

y = x^2 - 2x + 1

y = sqrt(x)

Here we have three functions. But, the output of each is called "y". If we start discussing these functions, how will you know which particular function I mean when I say "y"?

It's confusing, because they all have the same name.

This is the first benefit to function notation: it allows us to assign a unique name to each function:

f(x) = x + 4, so this function is now called f

g(x) = x^2 - 2x + 1, so this function is now called g

h(x) = sqrt(x), so this function is now called h

Having used function notation, if I talk about a value of g(x), you know right away that I'm referring to the value of y associated with the quadratic polynomial.

Another benefit is that function notation is concise.

I mean, we can express the value of x+4 (or any other named function) when x = 117 (for example) without doing any calculations.

Obviously, in the first function above, the value of y when x = 117 is 121, but let's pretend that we don't know that. How do we write the value of y when we don't know it?

This is how: f(117)

The expression f(117) is a constant.

The letter f is the name of the function.

The parentheses enclose the input to the function.

The output is expressed as f(117).

In other words, the notation f(117) represents the constant 121.

f(-4) represents the constant 0.

f(10) represents the constant 14.

f(x) represents the variable y. So the symbols x and f(x) are both variables.

Without function notation, I would need to write out all of the following.

The value of y when y = x + 4 and x is 117 is four more than 117, which is 121.

The value of y when y = x + 4 and x is -4 is four more than -4, which is 0.

The value of y when y = x + 4 and x is 10 is four more than 10, which is 10.

Having previously defined the three functions, function notation expresses these same statements completely much easier:

f(117) = 121

f(-4) = 0

f(10) = 14

What is the meaning of h(25) ?

It means the output that we get when we input 25 to function h.

In other words, it represents the value of y = sqrt(x) when x = 25.

It is much easier to simply say h(25) for the variable y, versus writing out the complete statement above.

The next advantage to function notation is that we can work SYMBOLICALLY. You'll come to understand this more, as you become familiar with function notation and after you begin to study composite functions, where the output from one function becomes the input to another function:

h[f(x)] = sqrt(x + 4)

Cheers ~ Mark

PS: The words "bear" and "bare" do not have the same meaning. Your subject line implies that you want us to take off our clothes, together!